Chapter 5

Elastic properties of

Zinc tris (thiourea) sulphate (ZTS)

single crystals.

5.1 Introduction

New nonlinear optical (NLO) frequency conversion materials with better physical

properties can have significant impact on laser technology [5.1], optical

communication [5.2], optical data storage technology [5.3] optical modulation etc.

Recent efforts at producing new frequency conversion materials have been focussed

primarily on increasing the NLO tensor de!! coefficients to produce structures that can

frequency double low peak power sources, such as diode lasers [5.4,5.5]. Also,

empha.sis has been given to develop highly transparent crystals suitable for frequency

conversion of high-power lasers such as those used for intemal confinement fusion

[5.6]. These applications have unique and often competing materials requirements and

illustrate that no single nonlinear optical material will be suitable for all these wide-

rangIng uses.

98

The search for new frequency conversion ~:r the past has been

concentrated primarily on organic compounds [5.4-5.8] and many NLO materials with

high nonlinear susceptibilities have been synthesized. However, the realization of

organic materials in the single c.rystal form in practical device applications has been

hindered by their inadequate transparency, poor optical quality, lack of robustness, low

laser damage threshold and above all, inability to grow large-size single crystals. The

molecules in pure organic crystals are often coupled by only relatively weak Van der

Waal's forces or hydrogen bonds, which result in poor mechanical properties.

Recently, a new class of materials known as metal organics or semi organics

have been developed which are metal complexes of highly polarisable organic

molecules having favorable physical properties such as high laser induced damage

resistance, good transparency, large nonlinearity in optical properties and ease of

single crystal growth. These are combinations of the properties of both organic and

inorganic crystal constituents. Recently, the NLO properties of some products of

thiourea [5.9-5.12] have attracted great interest. The thiourea molecule is an interesting

inorganic matrix modifier due to its large dipole moment [5.13] and has ability to form

an extensive network of hydrogen bonds. Unfortunately most thiourea complexes

known so far are centrosymmetric. Only a few crystallize into an acentric space group,

which is the most essential requirement of a material to be nonlinear optical.

A class of crystals incorporating urea and urea analogs in inorganic salts have

been grown already. Zinc tris(thiourea) sulphate (ZTS) with chemical formula

Zn[CS(NH2)2hS04, a prototype NLO coordination complex, has previously been

identified as a potentially useful material for frequency doubling of near-IR laser

radiation [5.9].

99

Structurally, ZTS crystal belongs to the orthorhombic system with space group

Pea2, (point group-mm2) and has four molecules per unit cell [5.14]. The lattice

parameters are reported to be a = 11.126 A, b = 7.773 A and c = 15.491 A. It has a less

prominent cleavage along the (100) plane. The Zinc ion is tetrahedrally cootdinated to

three sulfur atoms present in the thiourea molecules and to one oxygen atom attached

to a sulphate group. The thiourea molecules are planar and there is extensive

intennolecular and intra-molecular hydrogen bonding between thiourea, amino

hyd~ogen and sulphate oxygen [5.14,5.15]. The molecular structure and packing of the

molecules in the unit cell as viewed approximately along the [010] direction are shown

in Fig. 5.1 (a) and 5. l(b), respectively.

Spectroscopic studies on the metal complexes of thiourea such as bis(thiourea)

cadmium chloride and zinc tris(thiourea) sulphate single crystals have been reported in

literature [5.16,5.17]. It has also been reported that there exists two low temperature

phase transitions in ZTS, detected by Raman spectroscopic studies [5.15]. Raman

measurements show drastic changes around 60K and 122K indicating the presence of

two second-order phase transitions of order-disorder type. Ramabhadran et al. [5.18]

have studied the electrooptic, piezoelectric and dielectric properties of this crystal.

Reasons for its high polar nature [5.19] and high dielectric pennittivity at low

frequencies [5.20] are also reported in literature. Various thermal properties [5.21]

such as thermal diffusivity, heat capacity etc. and laser damage studies [5.21-5.23]

reveal that this crystal can be used in fabricating NLO devices.

100

Fig. 5.I(a): Molecular structure ofZTS

OS ®N eC o 0 ~ Zn o H

Fig. 5.I(b): Projection ofZTS crystal structure approximately along the [OIOJ direction

showing the alignment of the molecular dipoles (2n·0 bonds).

(Arrows point along the c-axis and indicate the net dipole moment. The upper right and

lower left molecules are below the plane of the upper left and lower right molecules.

For clarity hydrogen atoms have been omitted in this projection)

101

A preliminary report of optical transmission and measurement of second and

third order nonlinear optical (NLO) coefficients have been made by Newmann et al.

[5.24]. Subsequently the values of defT, Po and the threshold for SHG have been

reported [5.25]. The SHG efficiel,1cy, optical absorption, refractive index measurement,

calculation of phase matching loci, non-critical wavelengths and their experimental

verification have been done by Marcy et al. [5.9]. They have identified the principal

dielectric axes (a, p, y) and the ANSI / IEEE piezoelectric crystal coordinate system

(x, y, z) and the crystallographic axes (a, b, c). These axes are shown in Fig. 5.2.

b ex X

_aB Y

Fig. 5.2: Different systems of axes for ZTS crystals

It is also reported that the intensity of 0.532 ~m second ha111lonic generated on a per

particle basis by ZTS is about 1.2 times the intensity of that generated by potassium di-

hydrogen phosphate (KDP) having the same average diameter. This indicates that the

nonlinear coefflcients of Z1'S are similar to those of KDP. Much better prospects for

the practical application of Z1'S are found after achieving non-critical 1'ype-ll phase

102

matching (along the a-axis) by temperature tuning. It is expected that maXImum

conversion efficiency could be achieved with crystals of length 3-5 cm.

Single crystal growth, defect characterization and other related studies of this

crystal have been done by several researchers and reports are available in literature

[5.10,5.26-5.31]. Studies of the slip system, surface anisotropy in micro hardness and

its relation to inter atomic bonding are also investigated and reported [5.32,5.33].

It is reported that ZTS is thermodynamically stable up to 200°C following

thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC).

Temperature dependence of dielectric constant over the frequency range I-100kHz

show no anomaly, which further confirms its stability. Measurement of the thermal

expansion coefficient also does not indicate the presence of any structural phase

transition before its decomposition at about 200°C.

Single crystals of ZTS can be grown from aqueous solution either by the slow

evaporation or by the slow cooling techniques where thiourea and ZnS04.7H20 are

dissolved in the molar ratio ranging from 1: 1 to 6: 1. Since thiourea has the

coordinating capacity to form a variety of complexes, it would be safe to synthesize

ZTS first and then grow single crystals from solution after purification by several re­

crystallizations. A more detailed study of the crystal growth and scaling of ZTS has

been carried out by Cleveland Crystals Inc. in which crystals of size 13x 13x62 mm3

have been grown.

In this chapter we present the results of our measurement of the elastic

properties of this crystal. All the nine second-order elastic constants of ZTS have been

determined by measuring ultrasonic wave velocities along different symmetry

directions. Other related parameters such as Poisson's ratios, volume compressibility

etc. have also been determined. The phase velocity, group velocity and slowness

103

surfaces have been plotted in two dimensions to bring out the anisotropy in elastic

wave propagation in this crystal. Variation of a few elastic constants with temperature,

over a limited range are also presented. Details of the experimental technique, results

obtained and a discussion of the results are outlined in the following sections.

5.2 Sample preparation

ZTS material for crystal growth has been synthesized from zinc sulphate and thiourea

following the reaction

ZnS04 + 3 CS(NH2h 0 Zn[CS(NH2)2hS04.

ZnS04 and thiourea taken in the molar ratio 1:3 are dissolved separately in triply

distilled water, just sufficient to dissolve it. These solutions are mixed with vigorous

stirring to avoid the formation of other complexes. The resultant precipitate of ZTS is

washed and dried. This product obtained is purified by several re-crystallizations

before attempting to grow single crystals. Fig. 5.3 indicates the solubility of ZTS in

water at different temperatures, and one can see that the temperature coefficient of

solubility is positive, but rather small. This implies that the best method to grow big­

size single crystals is the slow evaporation technique, which is described already in

Chapter 2. Single crystals of size nearly 20x 18x 0.8mm3 have been grown over a

period of about 5 weeks. The prominent growth planes have been identified and the

morphology of the grown crystal is exhibited in Fig. 5.4. ZTS has a less prominent

cleavage along the (100) plane. The inter-planar angles have been measured using an

accurate contact goniometer and are compared with the values evaluated from

crystallographic data to identify the crystal directions and growth planes.

104

11

::::: 10 E

0 0

E 9

OIl '-'

.£ 8

:0 ;:l 7

"0 en

6

5 30 40 50 60 70 80

Temperature (Celsius)

Fig. 5.3: Solubility curve of ZTS in water

--o~ - -0-,

Fig. 5.4: Morphology of ZTS crystal grown from aqueous solution

105

The relative sizes of the growth planes can be expressed in the order {lOO} > {OO I} >

{ala} > {012} > {201} > {012} > {l10}. After identifying the crystallographic

directions, samples for measurements have been cut in the form of rectangular

parallelepipeds with a pair of parallel planes perpendicular to the a [100], b [010], c

[001], [110], [all] and [101] directions, as shown in Fig. 3.4 (in chapter 3) using a

slow speed diamond wheel saw. The planes of interest have been lightly polished

without spoiling the parallelism between the pair of planes.

5.3. Ultrasonic velocity measurements

Ultrasonic wave velocity measurements have been made along selected

crystallographic directions for waves of longitudinal and transverse polarizations. The

round-trip travel times through the sample cut along desired directions have been

measured accurately using the pulse echo overlap (PEO) technique, already described

in Chapter 2. To eliminate the errors introduced by the presence of the bonding

medium between the transducer and sample and the incorrect identification of the

condition of perfect match, McSkimin ~t correction has been applied. X and Y -cut

quartz transducers of resonant frequency 10MHz are used to generate ultrasonic wave

pulses and to detect the successive echoes after reflections from the rear end of the

sample. Eighteen different mode velocity measurements can be measured along these

specified directions. Out of this, twelve mode velocity measurements are sufficient to

evaluate all the nine second-order elastic constants with cross checks possible on some

of the critical values. Silicon grease is found to be a good bonding medium to fix the

transducer onto the crystal surface and to admit ultrasonic wave pulses generated by it

into the crystal medium. More technical details of these measurements are already

described in Chapter 2.

106

.5.4 Elastic constants of ZTS crystal

Velocities of propagation of ultrasonic waves through a medium are related to the

second order elastic constants and the relations are given in Table 5.1.

Table 5.1 Velocity of ultrasonic modes in ZTS crystals. L, T and QL represent

longitudinal, transverse and quasi-longitudinal modes respectively. The

relations between mode velocities and elastic constants are also given.

SI. Mode Direction of Direction of Measured Mode velocity -

No. propagation polarisation mode velocity elastic constant

relation (m/s)

1 L [100] [100] VI= 3259 ± 6 C - 2 II-PVI

2 L [010] [010] V2= 4151 ± 8 C - 2 22 - PV2

3 L [001] [001] V3= 3042 ± 6 C33 = pv/

4 T [010] [001] V4= 2066 ± 4 C - 2 44 - PV4

5 T [001] [010] V5= 2065 ± 4 C - 2 44 - PV5

6 T [100] [001] V6= 2064 ± 4 C55 = PV62

7 T [001] [100] V7= 2077 ± 4 C - 2 55 - PV7

8 T [100] [010] Vg= 2153 ± 4 C - 2 66 - pVg

9 T [010] [100] V9= 2135 ± 4 C - 2 66 - PV9

10 QL [110] [QL] VIO= 3863 ±8 C - [. (a) 12 - ab

11 QL [011] [QL] VII= 3985 ± 8 C - t; (b) 23 - be

12 QL [101 ] [QL] V12= 3241 ± 6 C - [. (c) 13 - ac •

107

(a) fab = {[c2 Cl I + S2 C66 - P Vlo2} {c2 C66 + S2 C22 - P Vlo2]/ C2S2} 112 - CM

(b) fbe = {[c2 C22 + S2 C44 - P V112} {c2 C44 + S2 C33 - P VI12]/ C2S2} 1/2 - C44

(c) fac = {[S2 CII + c2 Css - P VI/} {S2 Css + c2 C33 - P VI22]/ C2S2} 1/2 - Css

(Here c and s are the cosine and sine of the angle of rotation from the respective axes.)

[100], [010], and [001] directions are pure mode directions and hence each of the

velocities measured along these directions are related to only one elastic constant.

[110], [010], and [011] directions are mixed mode directions and hence the velocity of

propagation of ultrasonic waves along these directions are related to several elastic

constants. Ultrasonic wave velocities measured along different crystallographic

directions are listed in Table 5.1 with polarization of the mode of propagation. The

corresponding elastic stiffness constants, compliance constants and Poisson's ratios are

tabulated in Table 5.2.

Table 5.2 Elastic stiffuess constants, compliance constants and Poisson's ratios of ZTS

crystal at room temperature (300K)

Elastic stiffness constants Elastic compliance constants Poisson's

(GPa) (xl 0.10 m2 -N-1) ratios

CII = 19.65 ± 0.039 SII= 0.563 ± 0.001

C22 = 31.88 ± 0.064 S22= 0.388 ± 0.001 V12= 0.272

C33= 17.12 ±0.034 S33= 0.696 ± 0.001 V21 = 0.188

C44 = 7.89 ± 0.016 S44= 1.266 ± 0.003

Css= 7.88 ± 0.016 Sss= 1.269 ± 0.003 V23 = 0.257

C66= 8.58 ± 0.017 S66= 1.166 ± 0.002 V32 = 0.462

CI2= 7.19 ± 0.070 SI2= -0.106 ± 0.001

C23= 8.99 ± 0.090 S23= -0.179 ± 0.002 VI3 = 0.109

I CI3= 3.99 ± 0.040 SI3 = -0.076 ± 0.001 v31=0.135

108

The density of the crystal is measured to be 1850 Kg_m-3 _ The accuracy of the reported

elastic constant values is estimated to be better than 0_2% in the diagonal elastic

constants and 1 % in the case of off-diagonal elastic constants.

5.5 Temperature dependence of elastic constants

In order to study the dependence of ultrasonic wave velocities on temperature, the

crystal-transducer assembly is kept in an oven whose temperature is controlled

accurately. As the temperature changes, the condition of perfect matching of the

overlapped echoes changes. The tunable continuous wave oscillator is properly

adjusted to establish the previous condition of perfect matching and the frequency

output displayed on the frequency counter is noted. Temperature dependence of the

elastic constants CIl, C22 and C33 are shown in Fig. 5.5(a) and that ofC44, C55 and C66

are shown in Fig. 5.5(b).

5.6 Anisotropy in elastic wave propagation in ZTS In order to study the anisotropy of elastic properties of ZTS, various surface

plots such as the phase velocity, slowness, group velocity, Young's modulus and linear

compressibility have been drawn. The values of these parameters along the symmetry

planes a-b, b-c and a-c have been plotted to demonstrate the anisotropy in elastic

properties of this crystal. Sections of the phase velocity surfaces along the a-b, b-c and

a-c planes are plotted in Fig. 5.6(a), (b) and (c) respectively. The pure shear (PS),

quasi-shear (QS) and quasi-longitudinal (QL) modes are shown separately in each

diagram. These contours are almost circular in shape, which indicates that this crystal

does not show large-scale anisotropy in its ultrasonic (elastic) wave propagation

characteristics.

109

34

32

- 30 co Il..

28 (9

2 26 c ~ 24 I-rJ)

c 0 22 l-t.)

.S? 20 ..-rJ)

CO w 18

16

•••••••••••••••••• •• •• •• ••

•••••••••••••••••••• C" C ••••••

33

•••••••••••••••••••••••••• I

300 310 320 330 340 350 360 370

Temperature (K)

Fig.S.5(a) : Dependence of elastic constants Cl j, C22 and C33 on temperature.

8.6 ...... .... •• .- C 66 •• •• ~ 8.4 l- •• 0.. 0 • • '-' •• Vl ..... 8.2 •• c ~ •• ..... Vl • C 0 8.0 C)

C) •• •• •• C44 •• •• •• ..... • • •• Vl • •• •• ~ 7.8 •• -. • u.J •• •• •• •• 7.6 l- Css •• • ,

300 310 320 330 340 350

Temperature (K)

Fig.5.S(b) : Dependence of elastic constants C44 , C55 and C66 on temperature.

110

b

-1 0 1

Phase velocity (kmIs)

Fig. 5.6(a): Section of the phase velocity surfaces ofZTS along the a-b plane.

c

o/" .... ++++++++++~ + +oj,.

_+.... QL +'+.

* ~ t ~

: \

-4U-____ ~ ______ -L ______ L_ ____ _U

-4 -1 0 1

Phase velocity(kmls)

Fig. 5.6(b): Section of the phase velocity surfaces of ZTS along the b-c plane.

111

,q " o 0 0; > ~ .. .c "-

-4~----~----~----~----~ -4 -l 0

Phase veloClty (krnI~)

Fig. S.6(c): Section of the phase velocity surfaces ofZTS along the a-c plane

Fig. 5.7(a), (b) and (c) show sections of the slowness surfaces along the a-b, b-c

and a-c planes respectively, which are similar in nature. Ray velocity or group velocity

is the velocity of propagation of the energy, which need not be collinear with the

corresponding phase velocity. Sections of the ray velocity (group velocity) surface

along the a-b, b-c and a-c planes are shown in Fig. 5.8(a), (b) and (c) respectively.

-0.6 L--__ --L-I __ .....l-___ .L-.I __ ~ 1 __ --'1'-----'

-0.6 -0.4 -O.l O.l Q.4 0.6

Slowne~~ (~Ikm)

Fig. S.7(a): Section of the slowness surfaces ofZTS along the a-b plane

112

0.6 C

0.3 ,0+++-1-PS ++ '+--t.

i f ) .. .. b ., g 0 \ I ii5

"\ +T -0.3 +~.+ .. +*

-0.6 '-----'------'-------''------' -0.6 -0.3 0 0.3 0.6

Slowness (s/km)

Fig. S.7(b): Section of the slowness surfaces of ZTS along the b-c plane.

0.6 C

0.4

*+~+-lst- PS

O.J +T -t.+.

~ I "+. ~ r ) .. .. ., a ~ 0 \ J ii5

-0.) ++-4. ,+-F

""+++++-+-1"+-1'

-0.4

-0.6 -0.6 -0.4 -0.1 0 0.) 0.4 0.6

Slowness (s/km)

Fig. S.7(c): Section of the slowness surfaces ofZTS along the a-c plane.

113

b -+--+-

,j" .... -i< ,¥ -It /QL +

+ 'i;

f + ,.... + ~

! , -l;;

+ =f , .~

+ ~ ,

" + fa 0 0 , "'il + + > , 0- +

, + :3 , ,

0 + Cl i:

+ -J I-

-4 -J 0 J

Group velocity (kmIs)

Fig. 5.8(a): Section of the group velocity surfaces of ZTS along the a-b plane.

u.....----r---r----r----, c

J.J5 .... ! .~ " 0 "'il > 0-:3 0

Cl -J.J5

-405 '-----'-----'------'------' -405 -J.J5 0 J.J5 U

Group velocity (kmIs)

Fig. 5.8(b): Section of the group velocity surfaces of ZTS along the b-c plane.

114

c

-4 -J 0 J

GrOUp velocity (lcrr.ls)

Fig. 5.8( c): Section of the group velocity surfaces of ZTS along the a-c plane

These figures indicate that ZTS single crystals show somewhat isotropic behavior as

far as ultrasonic wave propagation is concerned.

Eq. 1.66 (in chapter 1) indicates that Young's modulus is a direction dependent

parameter and hence the shape of the surface generated by plotting Young's modulus

values for various directions will be very useful to demonstrate the anisotropy in

elastic properties. Sections of the Young's modulus surface. along the a-b, b-c and a-c

planes are shown in Fig. 5.9. The oval shape of these curves indicates the anisotropy in

Young's modulus.

The presence of the direction cosines I, m and 11 in Eq.1.74 also indicate that

the linear compressibility is also a direction dependent parameter. Sections of linear

compressibility surface along the a-b, b-c and a-c symmetry planes are shown in Fig.

5.10. These are not circular in shape and hence the compressibility of this crystal along

different directions in the crystal show clear anisotropy, when unit hydrostatic pressure

is applied.

115

db XXX

~o b-c +++

'«I' "- 'i<-j, e., + lA

\ ;3

"3 '0 0 0 ... 6 t lA

"bD § 0 >-

-JO

-JO 0 JO

Young's modulus (GPa)

Fig. 5.9: Sections of the Young's modulus surface of ZTS along the a-b (xxx), b-c (+++) and a-c (000) planes.

0.04

~ "'6 om

er' .::>

o ~ ,e ... ... .,

~ 8 -om ~

j -0.04

-0.04 -O.:J 0 om 0.04

Line&! :Jmpressibility (xl 0-9 m21N)

Fig. 5.10: Sections of the linear compressibility surface of ZTS along the a-b (xxx), b-c (+++) and a-c (000) planes.

116

5.7 Discussion and conclusion

All the nine second order elastic stiffness constants of Zinc tris(thiourea) sulphate

single crystals are reported for the first time. Velocities of propagation of ultrasonic

waves of both longitudinal and transverse nature along selected directions have been

measured with the maximum possible accuracy and necessary computations have been

done to evaluate all the nine second-order elastic stiffness and compliance constants of

this crystal. These constants along with Poisson's ratios are tabulated in Table 5.2. The

volume compressibility of this crystal has been evaluated using Eq. (1.71) as 0.926 x

1 0-IOm2~-1 and the corresponding bulk modulus is 10.8GPa.

Elastic constants CII, C22 and C33 are found to depend heavily on temperature.

Longitudinal tensions along a, band c directions cause the lattice to stretch along the

respective directions. This enhances thermal expansion of the lattice. As temperature

increases, the longitudinal strain corresponding to a fixed longitudinal stress increases,

resulting in a decrease in the elastic constant values. C44, Css and C66 depend much less

on temperature. Shearing caused by tangential forces and hence the corresponding

shear elastic constants are practically not much affected by increase in temperature. CS5

and C66 show a small decrease in their values with rise of temperature, whereas C44

remains practically unaffected.

Single crystals of ZTS grown from the aqueous solution are optically clear and

transparent. Our results indicate that ZTS does not show any large-scale anisotropy in

its elastic properties. Crystals are hard with no pronounced cleavage and hence are

suitable for device fabrication, if other properties meet the desired requirements.

117

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